Tuned Mass Damper

A Tuned Mass Damper (TMD) is a mechanical device, that you can buy at Flow Engineering, designed to add damping to a structure for a certain range of vibration frequencies. When properly designed, the extra damping will remove excessive movements of the structure. Feel free to contact us for more information or for your inquiry of a tuned mass damper system.

Working Principle of the Tuned Mass Damper

A Tuned Mass Damper (that you can order at our company) contains a suspended mass that is able to move in the same direction as the structure vibration direction. The oscillation frequency of the mass is tuned using either a spring system or pendulum system. When the structure starts to oscillate, the mass of the TMD mass will resonate with the vibration. A damper component connected between the structure and the TMD mass turns the kinetic energy of the structure into thermal energy, which dampens and lowers the amplitude of the structure. The design of an TMD depends on the oscillation frequency, mass of the structure, the direction of the movements (one horizontal direction, two horizontal directions, or vertical), and the available space.

Here you see a test configuration of one of our TMDs using a hydraulic actuator.

Design considerations

In simple situations a structure with a Tuned Mass Damper can be modeled as in the following figure.

Here k refers to the spring constant, c the damper constant, and m is the mass. Subscript 1 pertains to the structure and subscript 2 to the TMD.

A TMD can significantly reduce the response of a structure, as can be seen from the following graph.

The effects of varying several design parameters are given below.

Mass of Structure

Increasing the mass ratio μ (increasing the damper mass vs the mass of the vibrating structure) will decrease the structural displacement. The normalized structural displacement amplitude can be computed with the formula given by J.P. Den Hartog in “Mechanical Vibrations”:

As can be seen from the figure, Den Hartog’s approach, calculating with ζ1=0ζ1=0, is slightly conservative for steel structures (ζ1=0.2%ζ1=0.2%) at the lower mass ratios.

Damper Frequency

The eigenfrequencies of a structure may not be known to a sufficient level of accuracy at the time that the TMDs are designed. It is then useful to define a range in which the frequency of the eigenmode to be damped is sure to reside. By designing an appropriate Tuned Mass Damper for the entire range, the TMD can be designed and produced without the need for measuring the structure eigenfrequencies.

In the case that the structure has multiple eigenfrequencies relatively near to each other, a TMD with a wide effective frequency range may be used to add damping to several eigenmodes. Reducing the cost of the vibration damping system.

TMD Damping Ratio

The increase in amplitude from mis-tuned internal damping can be significant. It is because of this effect that we advise changing the internal dampers at set intervals of 15 to 25 years, depending on the damper used.

Our ongoing research into maintenance free Tuned Mass Dampers has solved this issue for linear tuned mass dampers. Buy our solution for linear Tuned Mass Dampers: Magnovisco Linear Dampers.